Question

system of equations is shown below.

y = -3x – 4

-9x – 3y = -2

Which statement about the ordered pair (1, -7) is true?
Responses
A It is not a solution to either equation.It is not a solution to either equation.
B It is the only solution to the system. It is the only solution to the system.
C It is one of many solutions to the system.It is one of many solutions to the system.
D It is a solution to the first but not the second equation.

Answer 1

To determine which statement about the ordered pair (1, -7) is true, we need to test whether this pair is a solution to each of the given equations.

1. **Testing the first equation:**

The first equation is:
\[
y = -3x - 4
\]

Substituting \(x = 1\) and \(y = -7\):
\[
-7 = -3(1) - 4
\]
\[
-7 = -3 - 4
\]
\[
-7 = -7
\]
This is true, so (1, -7) is a solution to the first equation.

2. **Testing the second equation:**

The second equation is:
\[
-9x - 3y = -2
\]

Substituting \(x = 1\) and \(y = -7\):
\[
-9(1) - 3(-7) = -2
\]
\[
-9 + 21 = -2
\]
\[
12 \neq -2
\]
This is false, so (1, -7) is not a solution to the second equation.

Now we can summarize our findings:
- (1, -7) is a solution to the first equation.
- (1, -7) is not a solution to the second equation.

Thus, the correct response is:

**D**: It is a solution to the first but not the second equation.